 | Charles William Hackley - 1846 - 542 σελίδες
...renders the result positive, then q is greater than the greatest root of the equation. Corollary 4. — Hence, if the signs of the alternate terms be changed,...positive, then — p is less than the least root. EXAMPLE. Find the initial figure in one of the roots of the equation Here one value of r does not differ... | |
 | Charles William Hackley - 1846 - 544 σελίδες
...renders the result positive, then q is greater than the greatest root of the equation. Corollary 4. — Hence, if the signs of the alternate terms be changed, and if p, and every quantity greater thau p, renders the result positive, then — p is less than the least root. EXAMPLE. Find the initial... | |
 | Charles William Hackley - 1847 - 546 σελίδες
...than the greatest root of the equation. Corollary 4. — Hence, if the signs of the alternate tei-ms be changed, and if p, and every quantity greater than...positive, then — p is less than the least root. EXAMPLE. Find the initial figure in one of the roots of the equation x3— 4^—6^+8 = 0. Here one... | |
 | Charles William Hackley - 1849 - 534 σελίδες
...renders the result positive, then q is greater than the greatest root of the equntion. Corollary 4. — Hence, if the signs of the alternate terms be changed, and if j>, and every quantity greater than p, renders the result positive, then — p is less than the least... | |
 | Joseph Ray - 1852 - 408 σελίδες
...render the results continually positive, q is greater than the greatest root of the equation. Cor. 4. Hence, if the signs of the alternate terms be changed,...result positive, then — p is less than the least root of the equation. Illustration. — If we form the equation whose roots are 5, 2. and —3, the result... | |
 | William Smyth - 1855 - 370 σελίδες
...equation, and will be a superior limit of the roots. 4°. Hence, if the signs of the alternate terms are changed, and if p and every quantity greater than...positive, then — p is less than the least root, and will be an inferior limit. 5°. If the degree of the equation be even, the substitution of a number... | |
 | Joseph Ray - 1857 - 408 σελίδες
...render the results continually positive, q is greater than the- greatest root of the equation. Cor. 4. Hence, if the signs of the alternate terms be changed,...greater than p, renders the result positive, then — y is less than the least root of the equation. Illustration. — If we form the equation -whose... | |
 | William Smyth - 1858 - 344 σελίδες
...equation, and will be a superior limit of the roots. 4°. Hence, if the signs of the alternate terms are changed, and if p and every quantity greater than p renders the result jrtsitive, then —p is less than the least root, and will be an inferior limit. 5°. If the degree... | |
 | Charles Hutton - 1860 - 1020 σελίδες
...g, renden the result positive, then q is greater than the greatest root of the equation. С :ir. 4. Hence, if the signs of the alternate terms be changed, and if p. ¿:u «very quantity greater than p, renders the result positive, then — pa les» ü-»¿ the least... | |
 | William Smyth - 1861 - 352 σελίδες
...equation, and will be a superior limit of the roots. 4°. Hence, if the signs of the alternate terms are changed, and if p and every quantity greater than...result positive, then —p is less than the least root, and will be an inferior limit. 5°. If the degree of the equation be even, the substitution of a number... | |
| |
Corollary 4. — Hence, if the signs of the alternate terms be changed, and if p, and every quantity greater than p, renders the result positive, then — p is less than the least root. 